Bellman functions and L^p estimates for paraproducts

Scientific paper - Original scientific paper

• Author: Vjekoslav Kovač
• Author: Kristina Ana Škreb
• Author's institution: University of Zagreb; Faculty of Civil Engineering
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Civil Engineering

Abstract (english)

We give an explicit formula for one possible Bellman function associated with the L^p boundedness of dyadic paraproducts regarded as bilinear operators or trilinear forms. Then we apply the same Bellman function in various other settings, to give self-contained alternative proofs of the estimates for several classical operators. These include the martingale paraproducts of Bañuelos and Bennett and the paraproducts with respect to the heat flows.

• Keywords (english): We give an explicit formula for one possible Bellman function associated with the L^p boundedness of dyadic paraproducts regarded as bilinear operators or trilinear forms. Then we apply the same Bellman function in various other settings, to give self-contained alternative proofs of the estimates for several classical operators. These include the martingale paraproducts of Bañuelos and Bennett and the paraproducts with respect to the heat flows.
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Probability and Mathematical Statistics-Poland
• Numbering: vol. 38(2), pp. 459-479
• e-ISSN: 0208-4147
• DOI: https://doi.org/10.19195/0208-4147.38.2.11
• URN:NBN: urn:nbn:hr:237:338921
• Publication: 2018
• Type of resource: Text
• Access conditions: Open access
• Created on: 2024-09-05 09:46:10